Let the per-minute fee be denoted as \( x \).
For Ross's first rental, he received a $10 discount and used the bike for 64 minutes. The total charge for that rental can be expressed as:
\[ \text{Total charge for first rental} = 64x - 10 \]
For the second rental, Ross used the bike for 39 minutes, and the total charge for this rental is:
\[ \text{Total charge for second rental} = 39x \]
According to the problem, both total charges are the same:
\[ 64x - 10 = 39x \]
To solve for \( x \), we can start by isolating \( x \). Subtract \( 39x \) from both sides:
\[ 64x - 39x - 10 = 0 \] \[ 25x - 10 = 0 \]
Next, we add 10 to both sides:
\[ 25x = 10 \]
Now, divide both sides by 25:
\[ x = \frac{10}{25} = \frac{2}{5} = 0.4 \]
Thus, the per-minute fee to rent an electric bike is
\[ \boxed{0.40} \text{ dollars per minute.} \]
We can verify this by checking the total charges for both rentals:
-
First rental charge:
- \( 64 \times 0.4 - 10 = 25.6 - 10 = 15.6 \)
-
Second rental charge:
- \( 39 \times 0.4 = 15.6 \)
Both charges are indeed equal, confirming that the calculation is correct. Thus, the per-minute fee is \( \boxed{0.40} \).